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arXiv · 1905.04375

Tropical diagrams of probability spaces

Rostislav Matveev·Jacobus W. Portegies
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Abstract

After endowing the space of diagrams of probability spaces with an entropy distance, we study its large-scale geometry by identifying the asymptotic cone as a closed convex cone in a Banach space. We call this cone the tropical cone, and its elements tropical diagrams of probability spaces. Given that the tropical cone has a rich structure, while tropical diagrams are rather flexible objects, we expect the theory of tropical diagrams to be useful for information optimization problems in information theory and artificial intelligence. In a companion article, we give a first application to derive a statement about the entropic cone.

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Rostislav Matveev, Jacobus W. Portegies. 2019-05-08. Tropical diagrams of probability spaces. https://arxiv.org/abs/1905.04375

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